Can believers live together peaceably when they differ on some personal issues of Christian living about which both have strong emotions?

Yes, we can because the Lord enjoined it (Mark 9:50), but only by applying Scriptural teaching to ourselves. The crux of the matter is not the right or wrong of another believers actions. Our behavior toward others is as important as their obedience to Christ. Another believers disobedience to truth doesnt justify our disobedience to the Lords command to love and serve our brother (John 13:34, 35). Showing him patiently and scripturally "a more excellent way" is loving service. Even when motivated by a desire to uphold truth, behavior directed against another believer denies significant truths.

Lowliness (regarding ourselves) and forbearance (regarding others) accompany the wisdom that produces peace (Ephesians 4:2, 3; James 3:17). Peace with my brother doesnt depend on his obedience to the Lord or on my obedience to my brother, but on my obedience to the Lord (Proverbs 16:7).